Consider a comet that is losing mass as it begins to orbit a planet. Does the mass of the comet affect its path? I have seen answers that say that the path will be affected. However, the change in kinetic energy of the comet as it comes closer to the planet is the same as the increase in gravitational potential energy. So because both equations include mass, I don't see how mass can affect the path of this comet. So how can the path of a comet be affected?
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$\begingroup$ The mass that is lost is also carrying away energy and momentum. A rocket is losing mass and energy, but uses the lost mass to generate a lot of momentum. Clearly how particularly the mass is lost will change the orbit. $\endgroup$– naturallyInconsistentCommented Sep 14 at 4:05
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If it was a sphere and its mass were lost symmetrically (same speed) in all directions, it would not affect its orbit (Assuming the planet is large enough so its motion would not to be affected by this mass loss)
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$\begingroup$ In the case of a comet, symmetric mass loss is not reasonable. $\endgroup$ Commented Sep 14 at 7:14
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$\begingroup$ @GiorgioP-DoomsdayClockIsAt-90 I am aware of that, it is for illustrative purposes, to show under what theoretical conditions an orbit would not change, otherwise the answer is yes, the orbit will change. $\endgroup$ Commented Sep 14 at 19:34